The invention concerns a method for comparing two recorded pixel images of the same rectangular format, called source images, representing in monochrome contrasted form, with E+1 possible contrast levels (E being a positive integer, for example equal to 255), equipotential lines of at least an integrated circuit chip.
It is known that it is possible to analyze defects of integrated circuits by comparing images which represent in monochrome contrasted form the potentials of the tracks of a chip, while the input ports of the integrated circuit are subjected to predetermined input signal vectors (cf., for example, xe2x80x9cFailure Analysis by dynamic voltage contrast development of a semi-automatic systemxe2x80x9d, N. GERAUD-LIVIA, G. PEREZ, A. CUQUEL, P. PERDU, ISTFA 1987, Los Angeles, pp. 67-73; thesis by M. P. PERDU, xe2x80x9cEtude de circuits intxc3xa9grxc3xa9s par contraste de potentiel: analyse des phxc3xa9nomxc3xa8nes de charge induits dans la couche de passivationxe2x80x9d, Universitxc3xa9 Paul Sabatier, No. 1740, 1994, pp. 1-50).
In the methods described hitherto, comparison of the source images presupposes data processing of the images (automatic analysis of brightness and contrast; simple mean through integration; smoothing of the digitized image; differential suppression of topographical information, interactive thresholding in three levels of gray by the operator on the color screen (trinarization), erosion, etc.).
The images are then superimposed and coordinated, either manually or by means of a computer, to disclose the location of the defect.
Nevertheless, in view of the highly complex nature of images of modern integrated circuits such as CMOS or BICMOS circuits, such semi-automatic methods, which still require a large amount of human intervention, are not sufficiently sophisticated, particularly in respect of their speed of execution and the accuracy of representation of the equipotentials.
Moreover, it is necessary to produce images for numerous electrical states (typically, from several hundreds to several tens of thousands) and, for each electrical state, a very large number of images to cover the entire surface of the same chip (several hundreds, or even several thousands). Human comparison of each pair of images, between a defective circuit and a reference circuit, is extremely time-consuming and tedious, even when alignment of the images is computer-assisted, and is therefore not sufficiently efficient to be applied on an industrial scale.
It should be noted, in this connection, that the integrated circuit manufacturing industry now requires that defective circuits be capable of being analyzed in a very rapid and systematic manner.
The object of the invention, therefore, is to overcome the above-mentioned disadvantages of the previous methods.
It is thus an object of the invention to propose a method for comparing images which can be automated to a large extent and be performed very rapidly and repeatedly on a multitude of images.
It is also an object of the invention to eliminate visual analysis of superimposed images by a human operator for the purpose of comparing them.
It is also an object of the invention to optimize the speed of processing of the images during this comparison.
It is also an object of the invention to propose a method which renders possible, in a simple and rapid manner, different image comparisons, particularly for searching for common equipotentials and/or equipotentials of the same form and location and of different potential states, and/or combination of equipotentials excluding common equipotentials, etc.
The invention, to achieve these objects, concerns a method for comparing two recorded pixel images of the same rectangular format, called source images, representing in monochrome contrasted form, with E+1 possible contrast levels, equipotential lines of at least an integrated circuit chip, characterized in that:
each source image is subjected to an adaptive thresholding processing with three distinct contrast levels, white, black and gray, called normal contrast levels, preferably corresponding respectively to the numerical values E, 0, and to an at least approximately median value between 0 and Exe2x80x94in particular, INT (E/2), INT being the integral number functionxe2x80x94so as to assign to each pixel of the image one of these three normal contrast levels,
an image, called the result image, is then formed from the thus processed source images by assigning to each pixel of the result image a normal contrast level selected from the three normal contrast levels of white, black and gray and determined in accordance with a predetermined logical rule of comparison, according to the nature of the comparison to be made, and in accordance with the normal contrast levels assigned to the corresponding pixels of the same location of the source images on completion of the adaptive thresholding processing.
Throughout the text, the normal contrast levels are for reasons of simplicity designated as white, gray and black, but it is understood that these qualifiers do not necessarily strictly designate the corresponding pure colors but, on the contrary, also include the case in which the contrast levels would be colored with the same dark color replacing the black and/or the same light color replacing the white. The invention is thus equally applicable in this case. Most generally, monochrome images such as those obtained by electronic microscope are, in practice, contrasted in black and white. Furthermore, in practice, it is sufficient to define a dark normal contrast level by a low value (which may or may not be equal to 0), a light contrast level by a high value (which may or may not be equal to E), and an intermediate contrast level by a median value.
The source images are formed of pixels, i.e., in the recording format generally referred to as xe2x80x9cbitmapxe2x80x9d. Such images can originate directly from a digital image processing system, or result from a digital conversion from a source image of a different recording format.
Advantageously, according to the invention, the adaptive thresholding processing of a source image comprising b columns of pixels and c rows of pixels is effected by:
defining, from the source image, a plurality of rectangles Ri,j formed of rectangular blocks of d rows of pixels and e columns of pixels, extracted from the source image, d less than c and e less than b, the rectangles Ri,j being defined to represent the source image in rows i of rectangles and columns j of rectangles,
calculating, for each rectangle Ri,j, the value of the minimum contrast level NGmin, the value of the maximum contrast level NGmax, the value of the mean contrast level NGmoy and the value of the standard deviation of the contrast levels ETNG of the different pixels of the rectangle Ri,j,
calculating the number of normal contrast levels having to be assigned to each rectangle Ri,j,
determining the value of each normal contrast level of each rectangle Ri,j,
establishing, for each rectangle Ri,j, a law for converting the actual contrast level of each pixel of the source image into a normal contrast level assigned to that pixel. A normal contrast level is then assigned to each pixel of each rectangle in accordance with this law, and the source image is reconstructed.
Each rectangle Ri,j is formed of a block of contiguous pixels, i.e., is formed of a rectangular portion of the source image.
The standard deviation ETNG is the square root of the variance. It is also possible to use the variance itself, which enables an operation to be eliminated, or any other particular standard deviation formula which represents the value of the deviations relative to the mean contrast level.
Advantageously, according to the invention, the rectangles Ri,j are defined so that:
each pair of rectangles Ri,j; Ri,j+1 which adjoin on the same row of rectangles overlap over half of their width, i.e., have a number of columns in common, of the order of e/2,
each pair of rectangles Ri,j; Ri+1,j which adjoin on the same column of rectangles overlap over half of their width, i.e., have a number of rows in common, of the order of d/2.
In particular, this overlapping of the rectangles makes it possible to avoid analysis errors due to the digital processing in very particular cases or, if such an error does occur, to correct its effects. Moreover, since each pixel is calculated several times (as belonging to several different rectangles (up to four if the boundaries are excluded or up to nine if they are included)), the numerical convergence of the method is assured in almost all cases.
Advantageously, according to the invention, d and e are selected so that if the minimum size of each object represented by the source image is a rectangle of g pixels in length and f pixels in width, fxe2x89xa6g, then:
10xe2x89xa6exe2x89xa610 f and 10xe2x89xa6dxe2x89xa610 g.
Advantageously, according to the invention, d and e are selected to be between 20 and 60, in particular, of the order of 40 for f and g between 5 and 15, in particular, of the order of 10. Advantageously, according to the invention, d and e are selected so that d/e=c/b. Thus, the shape of the rectangles Ri,j corresponds to that of the source image. For example, if the source image is square, the rectangles Ri,j are square.
Advantageously, according to the invention, the number of normal contrast levels NNG in each rectangle Ri,j is calculated by:
calculating the number of main peaks NP of the histogram curve of the actual contrast levels of the rectangle Ri,j, each peak corresponding to a maximum of the histogram curve,
defining the following conditions:
first condition: the histogram curve has at least three peaks,
second condition: NGmoyxe2x89xa7S1 and (NGmaxxe2x88x92NGmin)/NGmoyxe2x89xa7S2,
third condition: NGmaxxe2x88x92NGminxe2x89xa7S3 and ETNGxe2x89xa7S4,
fourth condition: the histogram curve has at least two peaks,
fifth condition: NGmaxxe2x88x92NGminxe2x89xa7S5 and ETNGxe2x89xa7S6,
wherein S1, S2, S3, S4, S5 and S6 are threshold values predetermined according to the type of integrated circuit represented by the source images and the characteristics of the image processing installation used for producing these source images,
sixth condition: the first condition and at least one of the second condition or the third condition are fulfilled,
seventh condition: the fourth condition and the fifth condition are fulfilled,
examining whether the sixth condition is fulfilled and, if such is the case, defining and recording the number of normal contrast levels NNG equal to three; if such is not the case, examining whether the seventh condition is fulfilled and, if such is the case, defining and recording the number of normal contrast levels NNG equal to two; if such is not the case, with neither the sixth nor the seventh condition being fulfilled, defining and recording the number of normal contrast levels NNG equal to one.
The threshold values S1, S2, S3, S4, S5, S6 can be defined experimentally according to the nature of the integrated circuits and corresponding source images.
Advantageously, according to the invention, for CMOS type integrated circuits with layout gauges of between 0.7xcexc and 1.5xcexc, S1 is selected to be of the order of 100; S2 of the order of 1.3; S3 of the order of 160; S4 of the order of 47; S5 of the order of 130; S6 of the order of 60.
Once the number of normal contrast levels has been determined, it is necessary to determine the value of each of them and to assign one of them to each pixel.
Advantageously, according to the invention, when the number of normal contrast levels NNG of at least one rectangle Ri,j of the source image is equal to three, a normal contrast level NCN is assigned to each pixel whose actual contrast level is NCR by:
separating the peaks of the histogram curve of the rectangle Ri,j by vertical boundaries passing through the minimum points between the peaks,
calculating by integration the area of each peak of the histogram curve of the rectangle Ri,j, selecting the three large peaks which have larger values, selecting from these three large peaks one peak, called the central peak, which is located between the two others and is delimited by a lower boundary FI and an upper boundary FS on the scale of contrast levels,
assigning the normal contrast level NCN equal to gray for any pixel whose actual contrast level NCR is included between the lower boundary FI and the upper boundary FS,
assigning the normal contrast level NCN equal to black for any pixel whose actual contrast level NCR is below the lower boundary FI,
assigning the normal contrast level NCN equal to white for any pixel whose actual contrast level NCR is above the upper boundary FS.
Moreover, for each rectangle Rixe2x80x2,jxe2x80x2 whose number of normal contrast levels NNG is less than or equal to 2, the value of this (these) normal contrast level(s) NNG is determined from a rectangle Ri,j comprising three previously assigned normal contrast levels, by assigning step-by-step the normal contrast levels of the pixels common to the rectangle(s) which overlap between the rectangles Ri,j and Rixe2x80x2,jxe2x80x2.
Advantageously, according to the invention, when no rectangle Ri,j has a number of normal contrast levels NNG equal to three, the rectangles Ri,j are processed one after the other, step-by-step, in successive stages, by comparing in each stage a zone, called the source zone, formed of at least one rectangle Ri,j having previously undergone such a stage, and a rectangle Ri,j having an overlap zone in common with the source zone.
Advantageously, according to the invention, when the number of normal contrast levels of all the rectangles Ri,j is equal to 1, the normal contrast level gray is assigned to all the pixels of the image.
Also advantageously, according to the invention, when the normal contrast levels have been assigned to all the pixels of a rectangle Ri,j, this rectangle Ri,j is subjected to a reduction processing, comprising a median filtering in the course of which each pixel is assigned the median value of the normal contrast levels of the set of pixels comprising this pixel and the pixels surrounding it.
Advantageously, according to the invention, the source image is reconstructed by reassembling the rectangles Ri,j, one after the other, in successive reassembly stages, from a gray image of the same format as the source image, and by executing, pixel by pixel, an extended OR logical rule OR+ between the image of the preceding stage and the rectangle Ri,j to be reassembled, by assigning to each pixel of the source image to be reconstructed the normal contrast level:
white if the pixels of the image of the preceding reassembly stage and of the rectangle Ri,j are, respectively, white and gray, or white and white;
black if the pixels of the image of the preceding reassembly stage and of the rectangle Ri,j are, respectively black and gray, or black and black;
gray in the other cases.
This reconstruction by successive extended OR logical rules OR+ allows resolution of any value discordances resulting from the median filtering processing on the rectangles.
The logical rules of comparison which can then be used in a method according to the invention are varied. Advantageously, according to the invention, a logical rule of comparison is used which is selected from the following logical rules of comparison:
extended AND function AND+: each pixel of the result image is assigned the normal contrast level:
black if the two corresponding pixels of the source images are black,
white if the two corresponding pixels of the source images are white,
gray in the other cases,
extended exclusive-OR function XOR+: each pixel of the result image is assigned the normal contrast level:
gray if the two corresponding pixels of the source images have the same normal contrast level,
white if the two corresponding pixels of the source images are white and gray, or white and black, or gray and black,
black if the two corresponding pixels of the source images are black and gray, or black and white, or gray and white. It is to be noted that the order of the source images is of importance for the extended exclusive xe2x88x92OR rule of comparison XOR+.
If it is wished to compare the differences between the images (equipotentials of the same form and location and of different potentials), a logical rule of comparison similar to the preceding rules can be used. Nevertheless, it is also possible to differentiate between complex pixelated images (with the actual contrast levels) by simple numerical means.
Thus, advantageously, according to the invention, at least one of the source images results from a differentiation stage performed previously between two images, called initial images, representing a surface portion of an integrated circuit chip, and in the course of which the actual contrast level NCR of each pixel of the source image is calculated from the actual contrast levels NCRA and NCRB of the corresponding pixels of the same location of the initial images, according to the formula: NCR=(NCRAxe2x88x92NCRB)/2+INT(E/2). INT represents the integral number function.
Moreover, prior to using a source image in an image comparison stage, an integration of this source image is performed on several identical photographs corresponding to this source image, and a median filtering is performed by assigning to each pixel the median value of the set of pixels formed by this pixel and the pixels surrounding it, so as to suppress the peaks due to noise.
Advantageously, according to the invention, integration and median filtering are performed on the initial images which are then differentiated to obtain a source image.
Also advantageously, according to the invention, the result image is subjected to a reduction processing comprising a median filtering consisting in assigning to each pixel the median value of the normal contrast levels of the set of pixels comprising this pixel and the pixels surrounding it, followed by an erosion and expansion processing for the normal contrast levels white and black.
The invention also concerns a method characterized by all or some of the characteristics mentioned above or below in combination.
The invention provides an extremely rapid and powerful method of comparison which in practice proves to be efficient for comparing images of integrated circuits, particularly such as those derived from systems of image processing by electronic microscopy applying potential contrast by secondary electron detection. It thus enables the methods of analyzing the defects of integrated circuits (tracing and physical characterization) to be accelerated and rendered reliable.